Velocity-space observation regions of high-resolution two-step reaction gamma-ray spectroscopy

High-resolution γ-ray spectroscopy (GRS) measurements resolve spectral shapes of Doppler-broadened γ-rays. We calculate weight functions describing velocity-space sensitivities of any two-step reaction GRS measurements in magnetized plasmas using the resonant nuclear reaction 9Be(α, nγ)12C as an example. The energy-dependent cross sections of this reaction suggest that GRS is sensitive to alpha particles above about 1.7 MeV and highly sensitive to alpha particles at the resonance energies of the reaction. Here we demonstrate that high-resolution two-step reaction GRS measurements are not only selective in energy but also in pitch angle. They can be highly sensitive in particular pitch angle ranges and completely insensitive in others. Moreover, GRS weight functions allow rapid calculation of γ-ray energy spectra from fast-ion distribution functions, additionally revealing how many photons any given alpha-particle velocity-space region contributes to the measurements in each γ-ray energy bin.